.. currentmodule:: statsmodels.tsa .. _tsa: Time Series analysis :mod:`tsa` =============================== :mod:`statsmodels.tsa` contains model classes and functions that are useful for time series analysis. This currently includes univariate autoregressive models (AR), vector autoregressive models (VAR) and univariate autoregressive moving average models (ARMA). It also includes descriptive statistics for time series, for example autocorrelation, partial autocorrelation function and periodogram, as well as the corresponding theoretical properties of ARMA or related processes. It also includes methods to work with autoregressive and moving average lag-polynomials. Additionally, related statistical tests and some useful helper functions are available. Estimation is either done by exact or conditional Maximum Likelihood or conditional least-squares, either using Kalman Filter or direct filters. Currently, functions and classes have to be imported from the corresponding module, but the main classes will be made available in the statsmodels.tsa namespace. The module structure is within statsmodels.tsa is - stattools : empirical properties and tests, acf, pacf, granger-causality, adf unit root test, ljung-box test and others. - ar_model : univariate autoregressive process, estimation with conditional and exact maximum likelihood and conditional least-squares - arima_model : univariate ARMA process, estimation with conditional and exact maximum likelihood and conditional least-squares - vector_ar, var : vector autoregressive process (VAR) estimation models, impulse response analysis, forecast error variance decompositions, and data visualization tools - kalmanf : estimation classes for ARMA and other models with exact MLE using Kalman Filter - arma_process : properties of arma processes with given parameters, this includes tools to convert between ARMA, MA and AR representation as well as acf, pacf, spectral density, impulse response function and similar - sandbox.tsa.fftarma : similar to arma_process but working in frequency domain - tsatools : additional helper functions, to create arrays of lagged variables, construct regressors for trend, detrend and similar. - filters : helper function for filtering time series Some additional functions that are also useful for time series analysis are in other parts of statsmodels, for example additional statistical tests. Some related functions are also available in matplotlib, nitime, and scikits.talkbox. Those functions are designed more for the use in signal processing where longer time series are available and work more often in the frequency domain. .. currentmodule:: statsmodels.tsa Descriptive Statistics and Tests """""""""""""""""""""""""""""""" .. autosummary:: :toctree: generated/ stattools.acovf stattools.acf stattools.pacf stattools.pacf_yw stattools.pacf_ols stattools.ccovf stattools.ccf stattools.periodogram stattools.adfuller stattools.q_stat stattools.grangercausalitytests stattools.levinson_durbin stattools.arma_order_select_ic x13.x13_arima_select_order x13.x13_arima_analysis Estimation """""""""" The following are the main estimation classes, which can be accessed through statsmodels.tsa.api and their result classes Univariate Autogressive Processes (AR) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. currentmodule:: statsmodels.tsa .. autosummary:: :toctree: generated/ ar_model.AR ar_model.ARResults Autogressive Moving-Average Processes (ARMA) and Kalman Filter ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. currentmodule:: statsmodels.tsa .. autosummary:: :toctree: generated/ arima_model.ARMA arima_model.ARMAResults arima_model.ARIMA arima_model.ARIMAResults kalmanf.kalmanfilter.KalmanFilter Vector Autogressive Processes (VAR) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. autosummary:: :toctree: generated/ vector_ar.var_model.VAR vector_ar.var_model.VARResults vector_ar.dynamic.DynamicVAR .. seealso:: tutorial :ref:`VAR documentation ` .. currentmodule:: statsmodels.tsa Vector Autogressive Processes (VAR) """"""""""""""""""""""""""""""""""" Besides estimation, several process properties and additional results after estimation are available for vector autoregressive processes. .. autosummary:: :toctree: generated/ vector_ar.var_model.VAR vector_ar.var_model.VARProcess vector_ar.var_model.VARResults vector_ar.irf.IRAnalysis vector_ar.var_model.FEVD vector_ar.dynamic.DynamicVAR .. seealso:: tutorial :ref:`VAR documentation ` ARMA Process """""""""""" The following are tools to work with the theoretical properties of an ARMA process for given lag-polynomials. .. autosummary:: :toctree: generated/ arima_process.ArmaProcess arima_process.ar2arma arima_process.arma2ar arima_process.arma2ma arima_process.arma_acf arima_process.arma_acovf arima_process.arma_generate_sample arima_process.arma_impulse_response arima_process.arma_pacf arima_process.arma_periodogram arima_process.deconvolve arima_process.index2lpol arima_process.lpol2index arima_process.lpol_fiar arima_process.lpol_fima arima_process.lpol_sdiff .. currentmodule:: statsmodels .. autosummary:: :toctree: generated/ sandbox.tsa.fftarma.ArmaFft .. currentmodule:: statsmodels.tsa Time Series Filters """"""""""""""""""" .. autosummary:: :toctree: generated/ filters.bk_filter.bkfilter filters.hp_filter.hpfilter filters.cf_filter.cffilter filters.filtertools.convolution_filter filters.filtertools.recursive_filter filters.filtertools.miso_lfilter filters.filtertools.fftconvolve3 filters.filtertools.fftconvolveinv TSA Tools """"""""" .. autosummary:: :toctree: generated/ tsatools.add_constant tsatools.add_trend tsatools.detrend tsatools.lagmat tsatools.lagmat2ds VARMA Process """"""""""""" .. autosummary:: :toctree: generated/ varma_process.VarmaPoly Interpolation """"""""""""" .. autosummary:: :toctree: generated/ interp.denton.dentonm